This invention pertains generally to sampled-data systems: systems containing at least a subsystem consisting of an analog input signal, some analog hardware, an analog-to-digital converter (ADC), a processing element such as a digital signal processor (DSP) and a processed output signal in digital form.
This invention pertains specifically to such systems in which the phase characteristic is sub optimum. Phase is of particular interest because while magnitude response specifications can often be stated clearly, phase specifications often cannot. Magnitude response specifications are often made directly in the frequency domain. In other words, the specifications are a specific statement of desired magnitude response at particular frequencies. Filters designed to compensate magnitude response are most often specified, designed, and evaluated in the frequency domain. However, this is not necessarily the case for phase. Generally speaking, the requirement for phase response is that it be linear. This is because group delay, which is just another way of looking at phase, is defined as:
                              GD          ⁡                      (            ω            )                          =                              -                                          ⅆ                                                                                              ⅆ                ω                                              ⁢                      Φ            ⁡                          (              ω              )                                                          Equation        ⁢                                  ⁢        1            where Φ is the phase. Group delay is the time delay that a frequency component experiences as it passes through a system. Linear, negative phase means that the group delay is a constant at all frequencies (i.e. the entire signal experiences only a time shift as it passes through the system). The statement of group delay and phase are essentially equivalent and both will be used interchangeably.